Let $\sigma$ and $b$ be Stefan's constant and Wien's constant respectively, then dimensions of $\sigma b$ are

At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire

A steel wire of length / has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is

The angle subtended by the vector $A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ with the $X$-axis is